A new empirical formula for the calculation of MS temperatures in pure iron and super-low carbon alloy steels

Journal of Materials Processing Technology 113 (2001) 556±562

A new empirical formula for the calculation of MS temperatures in pure iron and super-low carbon alloy steels Cheng Liua, Zhenbo Zhaoa, Derek O. Northwooda,*, Yunxu Liub a

Mechanical, Automotive and Materials Engineering, University of Windsor, Windsor, Ont., Canada N9B 3P4 b Materials Engineering, Jilin Institute of Technology, Jilin Province, Changchun 130012, PR China

Abstract It has often been observed that when the experimentally determined MS (the upper limit of the martensite transformation, or the practical start temperature of martensite transformation) temperatures are extrapolated to pure iron from binary Fe±C, Fe±Ni, Fe±Cr, Fe±Mn, Fe±Co alloys, anomalous temperatures, e.g. 520, 680, 700±750, 800±9008C, or even as high as the equilibrium g ! a temperature of 9128C, are obtained. In order to shed light on these con¯icting results, a new empirical formula MS … C† ˆ



795 525

25;000C1 45Mn 35V…Nb ‡ Zr ‡ Ti† 30Cr 20Ni 16Mo 8W 5Si ‡ 6Co ‡ 15Al 350…C2 0:005† 45Mn 35V…Nb ‡ Zr ‡ Ti† 30Cr 20Ni 16Mo 8W 5Si ‡ 6Co ‡ 15Al;

where

C1 < 0:005;

0:005  C2 < 0:02

is proposed to predict the MS temperature of pure iron and super-low carbon alloy steels. The effect of steel composition on the MS temperature is discussed. The validity of this new equation together with 11 other existing empirical formulae for the calculation of MS temperature in pure iron and super-low carbon alloy steels is examined. For more than 80% of super-low carbon alloy steels, the MS temperatures can be predicted by this new formula to within 258C. The new formula indicates an MS temperature of 7958C for a steel without carbon or other alloying elements (``pure'' iron). This is a better approximation to the experimental result of 7508C than for other formulae when the cooling rates exceed 35,0008C/s, and the carbon content is lower than 0.0017 wt.%. # 2001 Elsevier Science B.V. All rights reserved. Keywords: MS temperature; Pure iron; Super-low carbon alloy steels; Empirical formula

1. Introduction Due to the very low stability of super-cooled austenite in pure iron, the MS temperature for pure iron is usually determined only when different austenite-stabilizing elements are added, or a very fast cooling rate is applied. However, it has often been observed that when the experimentally determined MS temperatures are extrapolated to pure iron from binary Fe±C, Fe±Ni, Fe±Cr, Fe±Mn, Fe±Co alloys, anomalous temperatures, e.g. 5208C [1±4], 6808C [5], 700±7508C [6±12], 800±9008C [13], or even as high as the equilibrium g ! a temperature of 9128C [14], are obtained. Even if a very fast cooling rate is applied, the measured MS cannot always be considered to be a very reliable result since obtaining an ``absolutely'' pure iron

* Corresponding author. Present address: Faculty of Engineering and Applied Science, Ryerson Polytechnic University, Toronto, Ont., Canada M5B 2K3. Tel.: ‡1-416-979-5102; fax: ‡1-416-979-5308. E-mail address: [email protected] (D.O. Northwood).

(carbon free) is very dif®cult, and carbon analyses at low values are not always reliable [13]. In principle, the MS temperature for pure iron can be calculated by balancing the driving force for nucleation DGg!M against the available Fe chemical free energy change accompanying the transformation from austenite to martensite. However, calculation of the latter quantity involves the extrapolation of the free energy surfaces of austenite and ferrite into temperature regimes where they are not in thermodynamic equilibrium. Different analytical methods [15], assumptions and transformation parameters have to be considered in order to meet the different phase transformation conditions. This leads to uncertainties in calculated quantities. It has already been shown by Anderson and Hultgren [16] that the enthalpy data obtained by extrapolation involve an error that is of the same magnitude as the ®nal calculated driving force for the austenite±martensite transformation. Yeo [17] had also suggested that carbon-free alloys should be studied for a reassessment of the theories of martensite formation. Therefore, some questions related to MS temperatures of pure iron and super-low carbon alloy steels have also been examined.

0924-0136/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 4 - 0 1 3 6 ( 0 1 ) 0 0 6 2 5 - 2

C. Liu et al. / Journal of Materials Processing Technology 113 (2001) 556±562

2. Theoretical analysis and discussion 2.1. The critical points of the phase transformation for pure iron and the disadvantages of a thermodynamic method in calculating the MS temperature for pure iron The critical points of the phase transformation, Ae3 (where, the chemical free energy GgFe GaFe ˆ 0) for pure iron and T0 (where, the chemical free energy GgFe GM Fe ˆ 0) for plain martensite transformation should be totally different since the ®rst transformation involves the diffusion of iron atoms, whereas the martensite transformation is diffusionless, displacive or shear-like. In our opinion, Ae3 should be larger than T0 for pure iron and Ae3 T0 ˆ 60 65 C, even though some researchers propose Ae3 T0 ˆ 912 C. More detailed information on this particular topic can be found in the Ph.D. Dissertation of one of the authors [18]. It is well known that the MS temperature is closely related to T0. MS falls 2008C below T0 in the iron±carbon system when the carbon content changes from 0.05 to 1.3 wt.%, namely T0 MS ˆ 200 C (corresponding to a 1214 J/mol transformation driving force) [19]. However, for pure iron and super-low carbon steels, due to the lower coherency shear resistance, the driving force that is needed for the martensite transformation becomes smaller. Therefore, the difference between T0 and MS is reduced. No chemical factor energy terms are involved in the martensite transformation for pure iron. The total of nonchemical terms is no more than about 272 J/mol [19], i.e., a 458C difference in T0 and MS for pure iron. Although the general validity of the thermodynamic method is recognized, a new anomaly occurs (see Fig. 1

Fig. 1. Change in chemical free energy attending the austenite±martensite reaction in iron±carbon alloys as a function of temperature and carbon content [19].

557

[19]). The curves show the almost constancy of the free energy difference between martensite and austenite regardless of carbon content, and this implies that the driving force is always around 1214 J/mol. However, Bibby and Parr [13] found if the MS temperature for pure iron is not 5408C, but is in excess of 7508C, then, the driving force for the martensite transformation in pure iron will have to be considerably reduced. In fact, the data for 0.0 wt.% C iron was obtained from an extrapolation calculation, and no correct or reliable MS temperature was given in Cohen's [19] calculation (as shown in Fig. 1), since some data were not available to estimate the difference in the free energies of mixing between austenite and martensite. Cohen himself acknowledged that some assumptions must be introduced to make up this inadequacy [19]. Therefore, the simple extrapolation calculation of Bibby and Parr from Cohen's diagram is obviously unreasonable. Further, Singh and Parr [20] have shown that an e.m.f. is generated by a cell whose electrodes are equiaxed ferrite and martensite iron. This, in turn, demonstrates that the free energy of equiaxed ferrite is not the same as that of martensitic pure iron. Hence, an assumption that is implicit in the thermodynamic method for the martensitic transformation in Fe±C alloys [20] appears to be in error. 2.2. The effects of alloying elements on the MS temperature As mentioned in Section 1, the MS temperature for pure iron is often obtained by extrapolation to pure iron from binary alloys. Izumiyama et al. [21] ®rst showed the effect of individual alloying elements on the MS temperature for ironbased binary alloys with up to 13 elements (see solid lines in Fig. 2). Their results show that Al, Ti, V, Nb and Co effectively increase the MS temperature, whereas Si, Cu, Cr, Ni, Mn and C decrease the MS temperature. Extrapolation of their resulting data into zero content of the alloying element leads to a maximum MS temperature of about 7208C for pure iron. However, Liu's [22] study shows that all alloying elements (Mn, V, Ni, Cr, Mo, Cu, W, Si) except Al and Co decrease the MS temperature (see short dotted lines in Fig. 2). An MS temperature for pure iron of 7958C is obtained when Liu's data are extrapolated to zero alloying element content. The different effects of alloying elements on the MS temperature of iron-based binary alloys as determined by the other researchers is shown in Fig. 2 [7] (long dotted lines) and Fig. 3 [1,5,8±10,12,23±25]. It is seen that the effect of the same individual element on MS temperature is different since the different processing conditions (austenitizing conditions, cooling rates), impurity contents (especially, nitrogen: it is said that nitrogen has the similar effect on MS temperature to carbon [26]), and different grain sizes (the critical cooling rate is very sensitive to grain size [14]) have been used. Thus, very different values of the MS temperature for pure iron were observed when the different experimentally determined MS temperatures are extrapolated to pure iron [1±13,21±25]. Therefore,

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C. Liu et al. / Journal of Materials Processing Technology 113 (2001) 556±562

Fig. 2. MS temperature of iron-based binary alloys after Izumiyama et al. [21] (solid lines) and Liu [22] (short dotted lines) and Ackert and Parr [7] (long dotted lines).

an accurate MS temperature for pure iron cannot be obtained only by simple extrapolation, but by a more comprehensive analysis. 2.3. The effects of cooling rate on the martensitic transformation and MS temperature Another interesting phenomenon concerning the martensite transformation is the effects of cooling rate on the MS temperature. The work by Ansell et al. [27] shows an

Fig. 3. MS temperature of iron-based binary alloys as determined by various researchers [1,5,8±10,12,23±25].

increase in MS of 90±1228C in a sigmoidal fashion over a cooling rate ranging from 2750 to 24,8008C/s. The increase in MS was attributed to a reduced segregation of carbon to imperfections in austenite with increased cooling rate, and was correlated to the in¯uence of a third element on the diffusivity of carbon in austenite. Mirzayev and co-workers [28] further con®rmed that the continuous cooling transformation of steels is a multistage process. Several plateaus are exhibited and each plateau (stage) corresponds to a speci®c transformation product (microstructure), and each transformation product has its own transformation start temperature (or upper temperature limit) as shown in Fig. 4 [28]. An MS temperature of 400±5508C is obtained for 0.01 wt.% C iron from Fig. 4. However, in the very low alloying element or carbon concentration range, a relatively high MS temperature, 695±7508C, is obtained for Fe±17 ppm C and Fe± 15 ppm C alloys [7,13] (see Fig. 5). This is not surprising since the MS temperature is very sensitive to carbon content as discussed above. Therefore, Bibby and Parr [13] concluded that it is safe to assume that an MS of 5408C is associated with carbon contents between about 0.005 and 0.01%, rather than for pure iron, no matter what cooling rate is used. Zhao [14] provided an explanation for the above con¯ict in terms of the tendency of the critical cooling rate (CCR) to decrease with increasing alloying element content. He pointed out that in very dilute alloys, the CCR of massive ferrite is very high. The cooling rates used by most investigators are below the CCR of massive ferrite, so that their MS temperature is neither the true MS, nor even the true Ma (massive transformation start temperature), but a higher transformation start temperature for grain boundary ferrite (see Fig. 4). However, this explanation cannot provide

Fig. 4. Continuous cooling transformation start temperature versus cooling rate for iron containing about 0.01 wt.% C showing multistage nature of kinetics of the cooling transformation [28].

C. Liu et al. / Journal of Materials Processing Technology 113 (2001) 556±562

559

Fig. 5. The g ! a transformation in very dilute iron±carbon alloys (cooling rate range 0±50,0008C/s for solid lines [13] and cooling rate range 100±115,0008C/s for dotted lines [7]).

Fig. 6. The transformation start temperatures of g ! M, g ! a-W and g ! a in iron±carbon binary alloys.

a satisfactory answer for the behaviour shown in Fig. 5 [7,13] since martensite was observed at a higher cooling rate than massive ferrite. Bibby and Parr [13] thought that the MS temperature will be essentially independent of cooling rate, as long as this cooling rate is suf®cient to prevent any diffusion phenomena.

transformation start temperature should be 458C lower than the theoretical transformation start temperature since the nonchemical terms total is no more than about 272 J/mol [19]. For the g ! M martensite transformation, as discussed in Section 2.1, MS falls 2008C below T0 in the iron±carbon system when the carbon content changes from 0.05 to 1.3 wt.%. However, for pure iron, only a 458C decrease can be calculated from T0 to MS, similar to the g ! a-W transformation.

2.4. The similar transformation characteristics of martensite, bainite and acicular ferrite (Widmanstatten ferrite) for pure iron Martensite, bainite and acicular ferrite in pure iron can be considered as a same ``phase'' since they are formed by a similar diffusionless, displacive or shear-like process, and exhibit a coherent relationship with the parent phase. The transformation start temperature for pure iron should be same, namely, MS ˆ BS ˆ a-WS (the start temperature for Widmanstatten ferrite) since there is no effect of carbon or other chemical elements on the shear transformation process. As shown in Fig. 6, the theoretical …DG ˆ 0† and practical transformation start temperature can be summarized as: T0 (or Zg!M, at DGg!M ˆ 0) and MS for the g ! M martensite transformation; Zg!~a (at DGg!a ˆ 0) and a-WS for the g ! a-W (Widmanstatten ferrite) transformation; Ae3 (or Zg!a, at DGg!a ˆ 0); Ar3 for the g ! a diffusioncontrolled ferrite transformation. The practical transformation start temperature should be 5±108C lower than the theoretical value for the diffusion-controlled transformation [22]. However, for the g ! a-W (Widmanstatten ferrite) transformation, since only carbon is involved in the diffusion, rather than both carbon and iron atoms (iron atoms will transform in a diffusionless, displacive way), the practical

2.5. Comparison of formulae for predicting MS temperatures There have been several formulae which have been attempted to relate the MS temperature with alloy composition. These formulae are given in Table 1 [14,22,29±35] together with our new formula. The new formula indicates an MS temperature of 7958C for a steel without carbon or other alloying elements (``pure'' iron). This is a better approximation to the experimental result of 7508C than for other formulae (see Table 1, the other formulae predicted MS from 420 to 5618C for pure iron) when the cooling rates exceed 35,0008C/s, and the carbon content is lower than 0.0017 wt.% [13]. The temperature of 7958C is suf®ciently close to the quoted Curie temperature for iron (7708C) to remind one of Zener's [37] contention that f.c.c. iron should transform to the b.c.c. structure at the Curie temperature. However, we do not have an accurate value for the Curie temperature of high-purity iron. That's why Bibby and Parr [13] thought that MS temperature for pure iron would lie between 800 and 9008C after they extrapolated their very low carbon results to zero carbon. The validity of our new

560

No.

Source

Date, Reference

Equation

Calculated MS temperature for pure iron

Payson and Savage Carapella Rowland and Lyle Grange and Stewart Nehrenberg Steven and Haynes Andrew

1944, 1944, 1946, 1946, 1946, 1956, 1965,

8 9 10

Liu Liu Zhao

1981, [22] 1981, [22] 1992, [14]

499 496 499 538 499 561 539 512 550 538 420

11

Zhao

1992, [14]

12

Liu, Zhao, Northwood and Liu

2000

MS … C† ˆ 499 308C 32:4Mn 27Cr 16:2Ni 10:8Si 10:8Mo 10:8W MS … C† ˆ 496…1 0:62C†…1 0:092Mn†…1 0:0033Si†…1 0:045Ni†…1 0:07Cr†…1 0:029Mo†…1 0:018W†…1 ‡ 0:012Co† MS … C† ˆ 499 324C 32:4Mn 27Cr 16:2Ni 10:8Si 10:8Mo 10:8W MS … C† ˆ 538 350C 37:7Mn 37:7Cr 18:9Ni 27Mo MS … C† ˆ 499 292C 32:4Mn 22Cr 16:2Ni 10:8Si 10:8Mo MS … C† ˆ 561 474C 33Mn 17Cr 17Ni 21Mo MS … C† ˆ 539 423C 30:4Mn 12:1Cr 17:7Ni 7:5Mo …linear† MS … C† ˆ 512 453C 16:9Ni 9:5Mo ‡ 217…C†2 71:5…C†…Mn† ‡ 15Cr 67:6…C†…Cr† …nonlinear† MS … C† ˆ 550 361C 39Mn 35V 20Cr 17Ni 10Cu 5Mo 5W ‡ 16Co ‡ 30Al MS … C† ˆ 538 317C 33Mn 28Cr 17Ni 11Si 11Mo 11W MTM 208:33C 72:65N 43:36N2 16:08Ni ‡ 0:7817Ni2 0:02464Ni3 2:473Cr 33:428Mn S ˆ 420 ‡1:296Mn2 0:02167Mn3 ‡ 30:00Mo ‡ 12:86Co 0:2654Co2 ‡ 0:001547Co3 7:18Cu 16:28Ru ‡ 1:72Ru2 0:08117Ru3 a MLM 356:25C 260:64N 24:65Ni ‡ 1:36Ni2 0:0384Ni3 17:82Cr ‡ 1:42Cr2 47:59Mn ‡ 2:25Mn2 0:0415Mn3 S ˆ 540 ‡17:50Mo ‡ 21:87Co 0:468Co2 ‡ 0:00296Co3 16:52Cu 17:66Rub MS … C† ˆ 795 25; 000C 45Mn 35V…Nb ‡ Zr ‡ Ti† 30Cr 20Ni 16Mo 8W 5Si ‡ 6Co ‡ 15Al …for C < 0:005†

1 2 3 4 5 6 7

a b

[29] [30] [31] [32] [33] [34] [35]

MS temperature for twinned martensite. MS temperature for lath martensite.

MS … C† ˆ 525 350…C …for 0:005  C < 0:02†

0:005†

45Mn

35V…Nb ‡ Zr ‡ Ti†

30Cr

20Ni

16Mo

8W

5Si ‡ 6Co ‡ 15Al

540 795

C. Liu et al. / Journal of Materials Processing Technology 113 (2001) 556±562

Table 1 Chronological tabulation of formulas for calculating MS temperatures and application to pure iron

No.

Investigation

Experimental temperature (MS, 8C)

Cooling rate (8C/s)

Chemical composition (wt.%)

Calculated temperature (MS, 8C)

Derivation from experimental value (8C)

1 2 3 4 5 6 7 8 9 10 11

Esser et al. [4] Gilbert and Owen [1] Duwez [6] Srivastava and Parr [2] Bibby and Parr [13] Ackert and Parr [7] Ackert and Parr [7] Bibby [36] Ackert and Parr [7] Ackert and Parr [7] Ackert and Parr [7]

520 545 750 519 750 750 675 690 763a 550 590

18000 5500 12000 10000 >35000 >45000 ± ± ± ± ±

C: C: C: C: C: C: C: C: C: C: C:

521 523 770 524 753 758 673 673 780 520 522

‡1 22 ‡20 ‡5 ‡3 ‡8 2 17 ‡17 30 68

a

Average temperature between 725 and 8008C.

0.017, no record of metallic impurities 0.010, Si: 0.005, O2: 0.006, S: 0.004, P: 0.002 0.001, trace metallic impurities, each less than 0.001, O2 less than 0.02 0.005, Si: 0.02, Ni: 0.06 <0.0017, metallic impurities: 0.0015 0.0015, trace metallic impurities 0.0049, trace metallic impurities 0.0049 0.0006, trace metallic impurities 0.0186, trace metallic impurities 0.0141, trace metallic impurities

C. Liu et al. / Journal of Materials Processing Technology 113 (2001) 556±562

Table 2 MS values obtained experimentally and calculated using the new formula

561

562

C. Liu et al. / Journal of Materials Processing Technology 113 (2001) 556±562

equation for the calculation of MS temperature in super-low carbon alloy steels has been examined in more detail. For more than 80% of super-low carbon alloy steels, the MS temperatures can be predicted by this new formula to within 258C, as shown in Table 2. 3. Conclusions A new empirical formula is proposed to predict the MS temperature of the pure iron and super-low carbon alloy steels. The effects of steel composition and cooling rates on the MS temperatures are discussed. The similarity of the bainite, martensite, acicular ferrite transformation is summarized. For more than 80% of super-low carbon alloy steels, the MS temperatures can be predicted by this new formula to within 258C. The new formula indicates an MS temperature of 7958C for a steel without carbon or other alloying elements (``pure'' iron). This is a better approximation to the experimental result of 7508C than for other formulae when the cooling rates exceed 35,0008C/s, and the carbon content is lower than 0.0017 wt.%.

[9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28]

References [1] [2] [3] [4] [5] [6] [7] [8]

A. Gilbert, W.S. Owen, Acta Metall. 10 (1962) 45. L.P. Srivastava, J.G. Parr, TMS Ð AIME 224 (1962) 1295. A.B. Greninger, Trans. ASM 30 (1942) 100. H. Esser, et al., Arch. Eisenh. 6 (1933) 389. W.D. Swanson, J.G. Parr, JISI 202 (1964) 104. P. Duwez, Trans. AIME 191 (1951) 765. R.J. Ackert, J.G. Parr, JISI 209 (1971) 912. J.S. Pascover, S.V. Radcliffe, TMS Ð AIME 242 (1968) 673.

[29] [30] [31] [32] [33] [34] [35] [36] [37]

D.W. Gomersall, J.G. Parr, JISI 203 (1965) 275. J.G. Parr, JISI 205 (1967) 426. L. Kaufman, M. Cohen, Trans. AIME 206 (1956) 1393. L. Kaufman, M. Cohen, Progr. Metal Phys. 7 (1958) 165. M.J. Bibby, J.G. Parr, JISI 202 (1964) 100. J. Zhao, Mater. Sci. Technol. 8 (1992) 997. H.K.D.H. Bhadeshia, Met. Sci. 15 (1981) 178. P.D. Anderson, H. Hultgren, Trans. AIME 224 (1962) 842. R.B.G. Yeo, Trans. AIME 224 (1962) 1222. C. Liu, Ph.D. Dissertation, Harbin Institute of Technology, China, 1998. M. Cohen, E.S. Machlin, V.G. Paranjpe, Thermodynamics in Physical Metallurgy, ASM, 1949, p. 242. K.P. Singh, J.G. Parr, Acta Metall. 9 (1961) 1073. M. Izumiyama, M. Tsuchiya, Y. Imai, J. Japan Inst. Net. 34 (1974) 291. Y.X. Liu, Principle of Heat Treatment, China Mechanical Industry Press, Beijing, 1981. W.S. Owen, E.A. Wilson, Physical properties of martensite and bainite, Special Report No. 93, Iron and Steel Institute, London, 1965, p.153. E.A. Wilson, Ph.D. Thesis, University of Liverpool, 1965. R.H. Goodenow, R.F. Hehemann, Trans. TMS Ð AIME 233 (1965) 1777. C.Y. Kung, J.J. Rayment, Metall. Trans. A 13 (1982) 328. G.S. Ansell, S.J. Donachie, R.W. Messler Jr., Metall. Trans. 2 (1971) 2443. O.P. Morozov, D.A. Mirzayev, M.M. Shteynberg, Fiz. Met. Metalloved. 32 (1971) 1290. P. Payson, C.H. Savage, Trans. ASM 33 (1944) 261. L.A. Carapella, Met. Progr. 46 (1944) 108. E.S. Rowland, S.R. Lyle, Trans. ASM 37 (1946) 27. R.A. Grange, H.M. Stewart, Trans. AIME 167 (1946) 467. A.E. Nehrenberg, Trans. AIME 167 (1946) 494. W. Steven, A.G. Haynes, JISI 183 (1956) 349. K.W. Andrew, JISI 203 (1965) 721. M.J. Bibby, Master's Thesis, University of Alberta, 1963. C. Zener, Elasticity and Anelasticity, University of Chicago Press, 1952.